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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2511.11530 |
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| _version_ | 1866908653762641920 |
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| author | Pérez-Casany, Marta Duarte-López, Ariel Valero, Jordi |
| author_facet | Pérez-Casany, Marta Duarte-López, Ariel Valero, Jordi |
| contents | The Zipf distribution is a probability distribution widely used by scientists from various disciplines due to its ubiquity. Some of these areas include linguistics, physics, genetics, and sociology, among others. In this paper, it is proved that the Zipf distribution is both a mixture of geometric distributions and a mixture of zero-truncated Poisson distributions. It is also shown that it is not the zero-truncation of a mixed Poisson distribution. These results are important because they provide insights on the data generation mechanism that leads to data from a Zipf distribution. Additionally, it is proved, as a corollary, that the Zipf-Poisson Stopped Sum distribution is a particular case of a mixed Poisson distribution. The results are illustrated analyzing the 135 chapters of the novel Moby Dick. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11530 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring the Zipf Distribution Through the Lens of Mixtures Pérez-Casany, Marta Duarte-López, Ariel Valero, Jordi Statistics Theory 62E10, 60E05 G.3 The Zipf distribution is a probability distribution widely used by scientists from various disciplines due to its ubiquity. Some of these areas include linguistics, physics, genetics, and sociology, among others. In this paper, it is proved that the Zipf distribution is both a mixture of geometric distributions and a mixture of zero-truncated Poisson distributions. It is also shown that it is not the zero-truncation of a mixed Poisson distribution. These results are important because they provide insights on the data generation mechanism that leads to data from a Zipf distribution. Additionally, it is proved, as a corollary, that the Zipf-Poisson Stopped Sum distribution is a particular case of a mixed Poisson distribution. The results are illustrated analyzing the 135 chapters of the novel Moby Dick. |
| title | Exploring the Zipf Distribution Through the Lens of Mixtures |
| topic | Statistics Theory 62E10, 60E05 G.3 |
| url | https://arxiv.org/abs/2511.11530 |